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= Theory =
{{Infobox ET}}
35-tET or 35-[[EDO]] refers to a tuning system which divides the octave into 35 steps of approximately [[cent|34.29¢]] each.
{{ED intro}}


As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal edos]]: [[5edo]] and [[7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢. Because it includes 7edo, 35edo tunes the 29th harmonic with +1 cent of error. 35edo can also represent the 2.3.5.7.11.17 [[Just_intonation_subgroups|subgroup]] and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators (7/5 and 17/11 stand out, having less than 1 cent error). Therefore among whitewood tunings it is very versatile; you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore [[22edo]]'s more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for [[greenwood]] and [[secund]] temperaments, as well as 11-limit [[muggles]], and the 35f val is an excellent tuning for 13-limit muggles. 35edo is the largest edo with a lack of a diatonic scale.
== Theory ==
As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal edos]]: [[5edo]] and [[7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71{{c}} and 5edo's wide fifth of 720{{c}}. Because it includes 7edo, 35edo tunes the 29th harmonic with only 1{{c}} of error.


=Notation=
35edo can also represent the 2.3.5.7.11.17 [[subgroup]] and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators (7/5 and 17/11 stand out, having less than 1 cent error). Therefore among [[whitewood]] tunings it is very versatile; you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore [[22edo]]'s more in-tune versions of 35edo MOS's and consistent representation of both subgroups.


35edo has the optimal [[patent val]] for [[greenwood]] and [[secund]] temperaments, as well as 11-limit [[muggles]], and the 35f val is an excellent tuning for 13-limit muggles. 35edo is the largest edo with a lack of a [[diatonic scale]] (unless 7edo is considered a diatonic scale).
=== Odd harmonics ===
{{Harmonics in equal|35}}
== Notation ==
The 7edo fifth is preferred as the diatonic generator for ups and downs notation due to being much easier to notate than the 5edo fifth (which involves E and F being enharmonic), as well as being closer to 3/2.
{| class="wikitable"
{| class="wikitable"
|-
|-
! style="text-align:center;" | Degrees
! Degrees
! style="text-align:center;" | Cents
! Cents
! colspan="3" style="text-align:center;" | [[Ups_and_Downs_Notation|Up/down]] [[Ups_and_Downs_Notation|Notation]]
! colspan="3" | [[Ups and downs notation]]
! [[Dual-fifth tuning|Dual-fifth]] notation
<small>based on closest 12edo interval</small>
|-
|-
| style="text-align:center;" | 0
| 0
| style="text-align:center;" | 0.000
| 0.000
| style="text-align:center;" | unison
| unison
| style="text-align:center;" | 1
| 1
| style="text-align:center;" | D
| D
| 1sn, prime
|-
|-
| style="text-align:center;" | 1
| 1
| style="text-align:center;" | 34.286
| 34.286
| style="text-align:center;" | up unison
| up unison
| style="text-align:center;" | ^1
| ^1
| style="text-align:center;" | ^D
| ^D
| augmented 1sn
|-
|-
| style="text-align:center;" | 2
| 2
| style="text-align:center;" | 68.571
| 68.571
| style="text-align:center;" | double-up unison
| dup unison
| style="text-align:center;" | ^^1
| ^^1
| style="text-align:center;" | ^^D
| ^^D
| diminished 2nd
|-
|-
| style="text-align:center;" | 3
| 3
| style="text-align:center;" | 102.857
| 102.857
| style="text-align:center;" | double-down 2nd
| dud 2nd
| style="text-align:center;" | vv2
| vv2
| style="text-align:center;" | vvE
| vvE
| minor 2nd
|-
|-
| style="text-align:center;" | 4
| 4
| style="text-align:center;" | 137.143
| 137.143
| style="text-align:center;" | down 2nd
| down 2nd
| style="text-align:center;" | v2
| v2
| style="text-align:center;" | vE
| vE
| neutral 2nd
|-
|-
| style="text-align:center;" | 5
| 5
| style="text-align:center;" |171.429
| 171.429
| style="text-align:center;" | 2nd
| 2nd
| style="text-align:center;" | 2
| 2
| style="text-align:center;" | E
| E
| submajor 2nd
|-
|-
| style="text-align:center;" | 6
| 6
| style="text-align:center;" | 205.714
| 205.714
| style="text-align:center;" | up 2nd
| up 2nd
| style="text-align:center;" | ^2
| ^2
| style="text-align:center;" | ^E
| ^E
| major 2nd
|-
|-
| style="text-align:center;" | 7
| 7
| style="text-align:center;" | 240
| 240
| style="text-align:center;" | double-up 2nd
| dup 2nd
| style="text-align:center;" | ^^2
| ^^2
| style="text-align:center;" | ^^E
| ^^E
| supermajor 2nd
|-
|-
| style="text-align:center;" | 8
| 8
| style="text-align:center;" | 274.286
| 274.286
| style="text-align:center;" | double-down 3rd
| dud 3rd
| style="text-align:center;" | vv3
| vv3
| style="text-align:center;" | vvF
| vvF
| diminished 3rd
|-
|-
| style="text-align:center;" | 9
| 9
| style="text-align:center;" | 308.571
| 308.571
| style="text-align:center;" | down 3rd
| down 3rd
| style="text-align:center;" | v3
| v3
| style="text-align:center;" | vF
| vF
| minor 3rd
|-
|-
| style="text-align:center;" | 10
| 10
| style="text-align:center;" |342.857
| 342.857
| style="text-align:center;" | 3rd
| 3rd
| style="text-align:center;" | 3
| 3
| style="text-align:center;" | F
| F
| neutral 3rd
|-
|-
| style="text-align:center;" | 11
| 11
| style="text-align:center;" | 377.143
| 377.143
| style="text-align:center;" | up 3rd
| up 3rd
| style="text-align:center;" | ^3
| ^3
| style="text-align:center;" | ^F
| ^F
| major 3rd
|-
|-
| style="text-align:center;" | 12
| 12
| style="text-align:center;" | 411.429
| 411.429
| style="text-align:center;" | double-up 3rd
| dup 3rd
| style="text-align:center;" | ^^3
| ^^3
| style="text-align:center;" | ^^F
| ^^F
| augmented 3rd
|-
|-
| style="text-align:center;" | 13
| 13
| style="text-align:center;" | 445.714
| 445.714
| style="text-align:center;" | double-down 4th
| dud 4th
| style="text-align:center;" | vv4
| vv4
| style="text-align:center;" | vvG
| vvG
| diminished 4th
|-
|-
| style="text-align:center;" | 14
| 14
| style="text-align:center;" | 480
| 480
| style="text-align:center;" | down 4th
| down 4th
| style="text-align:center;" | v4
| v4
| style="text-align:center;" | vG
| vG
| minor 4th
|-
|-
| style="text-align:center;" | 15
| 15
| style="text-align:center;" |514.286
| 514.286
| style="text-align:center;" | 4th
| 4th
| style="text-align:center;" | 4
| 4
| style="text-align:center;" | G
| G
| major 4th
|-
|-
| style="text-align:center;" | 16
| 16
| style="text-align:center;" | 548.571
| 548.571
| style="text-align:center;" | up 4th
| up 4th
| style="text-align:center;" | ^4
| ^4
| style="text-align:center;" | ^G
| ^G
| augmented 4th
|-
|-
| style="text-align:center;" | 17
| 17
| style="text-align:center;" | 582.857
| 582.857
| style="text-align:center;" | double-up 4th
| dup 4th
| style="text-align:center;" | ^^4
| ^^4
| style="text-align:center;" | ^^G
| ^^G
| minor tritone
|-
|-
| style="text-align:center;" | 18
| 18
| style="text-align:center;" | 617.143
| 617.143
| style="text-align:center;" | double-down 5th
| dud 5th
| style="text-align:center;" | vv5
| vv5
| style="text-align:center;" | vvA
| vvA
| major tritone
|-
|-
| style="text-align:center;" | 19
| 19
| style="text-align:center;" | 651.429
| 651.429
| style="text-align:center;" | down 5th
| down 5th
| style="text-align:center;" | v5
| v5
| style="text-align:center;" | vA
| vA
| diminished 5th
|-
|-
| style="text-align:center;" | 20
| 20
| style="text-align:center;" |685.714
| 685.714
| style="text-align:center;" | 5th
| 5th
| style="text-align:center;" | 5
| 5
| style="text-align:center;" | A
| A
| minor 5th
|-
|-
| style="text-align:center;" | 21
| 21
| style="text-align:center;" | 720
| 720
| style="text-align:center;" | up 5th
| up 5th
| style="text-align:center;" | ^5
| ^5
| style="text-align:center;" | ^A
| ^A
| major 5th
|-
|-
| style="text-align:center;" | 22
| 22
| style="text-align:center;" | 754.286
| 754.286
| style="text-align:center;" | double-up 5th
| dup 5th
| style="text-align:center;" | ^^5
| ^^5
| style="text-align:center;" | ^^A
| ^^A
| augmented 5th
|-
|-
| style="text-align:center;" | 23
| 23
| style="text-align:center;" | 788.571
| 788.571
| style="text-align:center;" | double-down 6th
| dud 6th
| style="text-align:center;" | vv6
| vv6
| style="text-align:center;" | vvB
| vvB
| diminished 6th
|-
|-
| style="text-align:center;" | 24
| 24
| style="text-align:center;" | 822.857
| 822.857
| style="text-align:center;" | down 6th
| down 6th
| style="text-align:center;" | v6
| v6
| style="text-align:center;" | vB
| vB
| minor 6th
|-
|-
| style="text-align:center;" | 25
| 25
| style="text-align:center;" |857.143
| 857.143
| style="text-align:center;" | 6th
| 6th
| style="text-align:center;" | 6
| 6
| style="text-align:center;" | B
| B
| neutral 6th
|-
|-
| style="text-align:center;" | 26
| 26
| style="text-align:center;" | 891.429
| 891.429
| style="text-align:center;" | up 6th
| up 6th
| style="text-align:center;" | ^6
| ^6
| style="text-align:center;" | ^B
| ^B
| major 6th
|-
|-
| style="text-align:center;" | 27
| 27
| style="text-align:center;" | 925.714
| 925.714
| style="text-align:center;" | double-up 6th
| dup 6th
| style="text-align:center;" | ^^6
| ^^6
| style="text-align:center;" | ^^B
| ^^B
| augmented 6th
|-
|-
| style="text-align:center;" | 28
| 28
| style="text-align:center;" | 960
| 960
| style="text-align:center;" | double-down 7th
| dud 7th
| style="text-align:center;" | vv7
| vv7
| style="text-align:center;" | vvC
| vvC
| diminished 7th
|-
|-
| style="text-align:center;" | 29
| 29
| style="text-align:center;" | 994.286
| 994.286
| style="text-align:center;" | down 7th
| down 7th
| style="text-align:center;" | v7
| v7
| style="text-align:center;" | vC
| vC
| minor 7th
|-
|-
| style="text-align:center;" | 30
| 30
| style="text-align:center;" |1028.571
| 1028.571
| style="text-align:center;" | 7th
| 7th
| style="text-align:center;" | 7
| 7
| style="text-align:center;" | C
| C
| superminor 7th
|-
|-
| style="text-align:center;" | 31
| 31
| style="text-align:center;" | 1062.857
| 1062.857
| style="text-align:center;" | up 7th
| up 7th
| style="text-align:center;" | ^7
| ^7
| style="text-align:center;" | ^C
| ^C
| neutral 7th
|-
|-
| style="text-align:center;" | 32
| 32
| style="text-align:center;" | 1097.143
| 1097.143
| style="text-align:center;" | double-up 7th
| dup 7th
| style="text-align:center;" | ^^7
| ^^7
| style="text-align:center;" | ^^C
| ^^C
| major 7th
|-
|-
| style="text-align:center;" | 33
| 33
| style="text-align:center;" | 1131.429
| 1131.429
| style="text-align:center;" | double-down 8ve
| dud 8ve
| style="text-align:center;" | vv8
| vv8
| style="text-align:center;" | vvD
| vvD
| augmented 7th
|-
|-
| style="text-align:center;" | 34
| 34
| style="text-align:center;" | 1165.714
| 1165.714
| style="text-align:center;" | down 8ve
| down 8ve
| style="text-align:center;" | v8
| v8
| style="text-align:center;" | vD
| vD
| diminished 8ve
|-
|-
| style="text-align:center;" | 35
| 35
| style="text-align:center;" | 1200
| 1200
| style="text-align:center;" | 8ve
| 8ve
| style="text-align:center;" | 8
| 8
| style="text-align:center;" | D
| D
| 8ve
|}
|}


==Chord Names==
===Sagittal notation===
====Best fifth notation====
This notation uses the same sagittal sequence as EDOs [[30edo#Second-best fifth notation|30b]] and [[40edo#Sagittal notation|40]], and is a superset of the notation for [[7edo#Sagittal notation|7-EDO]].
 
<imagemap>
File:35-EDO_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 415 0 575 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 415 106 [[Fractional_3-limit_notation#Bad-fifths_limma-fraction_notation | limma-fraction notation]]
default [[File:35-EDO_Sagittal.svg]]
</imagemap>
 
====Second-best fifth notation====
This notation uses the same sagittal sequence as [[42edo#Sagittal notation|42-EDO]], and is a superset of the notation for [[5edo#Sagittal notation|5-EDO]].
 
<imagemap>
File:35b_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 391 0 551 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 391 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:35b_Sagittal.svg]]
</imagemap>
 
=== Chord Names ===
Ups and downs can be used to name 35edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. An up or down immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are.
Ups and downs can be used to name 35edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. An up or down immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are.


Line 250: Line 321:
0-9-20-29 = C vE G vB = Cv7 = C down seven
0-9-20-29 = C vE G vB = Cv7 = C down seven


For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].
For a more complete list, see [[Ups and downs notation#Chords and Chord Progressions|Ups and downs notation - Chords and Chord Progressions]].


=JI Intervals=
== JI Intervals ==
(Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.)
(Bolded ratio indicates that the ratio is most accurately tuned by the given 35edo interval.)


{| class="wikitable"
{| class="wikitable"
|-
|-
! | Degrees
| Degrees
! | Cents value
| Cents value
! | Ratios in 2.5.7.11.17 subgroup
| Ratios in 2.5.7.11.17 subgroup
! | Ratios with flat 3
| Ratios with flat 3
! | Ratios with sharp 3
| Ratios with sharp 3
! | Ratios with best 9
| Ratios with best 9
|-
|-
| | 0
| 0
| 0.000
| 0.000
| | '''1/1'''
| '''1/1'''
| | (see comma table)
| (see comma table)
| |  
|  
| |  
|  
|-
|-
| | 1
| 1
| | 34.286
| 34.286
| | '''50/49''', '''121/119''', 33/32
| '''50/49''', '''121/119''', 33/32
| | '''36/35'''
| '''36/35'''
| | 25/24
| 25/24
| | '''81/80'''
| '''81/80'''
|-
|-
| | 2
| 2
| | 68.571
| 68.571
| | 128/125
| 128/125
| | '''25/24'''
| '''25/24'''
| | 81/80
| 81/80
| |  
|  
|-
|-
| | 3
| 3
| | 102.857
| 102.857
| | '''17/16'''
| '''17/16'''
| | '''15/14'''
| '''15/14'''
| | '''16/15'''
| '''16/15'''
| | '''18/17'''
| '''18/17'''
|-
|-
| | 4
| 4
| | 137.143
| 137.143
| |  
|  
| | '''12/11''', 16/15
| '''12/11''', 16/15
| |  
|  
| |  
|  
|-
|-
| | 5
| 5
| |171.429
|171.429
| | '''11/10'''
| '''11/10'''
| |  
|  
| | 12/11
| 12/11
| | '''10/9'''
| '''10/9'''
|-
|-
| | 6
| 6
| | 205.714
| 205.714
| |  
|  
| |  
|  
| |  
|  
| | '''9/8'''
| '''9/8'''
|-
|-
| | 7
| 7
| | 240
| 240
| | '''8/7'''
| '''8/7'''
| |  
|  
| | 7/6
| 7/6
| |  
|  
|-
|-
| | 8
| 8
| | 274.286
| 274.286
| | '''20/17'''
| '''20/17'''
| | '''7/6'''
| '''7/6'''
| |  
|  
| |  
|  
|-
|-
| | 9
| 9
| | 308.571
| 308.571
| |  
|  
| | '''6/5'''
| '''6/5'''
| |  
|  
| |  
|  
|-
|-
| | 10
| 10
| |342.857
|342.857
| | '''17/14'''
| '''17/14'''
| |  
|  
| | 6/5
| 6/5
| | '''11/9'''
| '''11/9'''
|-
|-
| | 11
| 11
| | 377.143
| 377.143
| | '''5/4'''
| '''5/4'''
| |  
|  
| |  
|  
| |  
|  
|-
|-
| | 12
| 12
| | 411.429
| 411.429
| | '''14/11'''
| '''14/11'''
| |  
|  
| |  
|  
| |  
|  
|-
|-
| | 13
| 13
| | 445.714
| 445.714
| | '''22/17''', 32/25
| '''22/17''', 32/25
| |  
|  
| |  
|  
| | '''9/7'''
| '''9/7'''
|-
|-
| | 14
| 14
| | 480
| 480
| |  
|  
| |  
|  
| | 4/3, '''21/16'''
| 4/3, '''21/16'''
| |  
|  
|-
|-
| | 15
| 15
| |514.286
|514.286
| |  
|  
| | '''4/3'''
| '''4/3'''
| |  
|  
| |  
|  
|-
|-
| | 16
| 16
| | 548.571
| 548.571
| | '''11/8'''
| '''11/8'''
| |  
|  
| |  
|  
| |  
|  
|-
|-
| | 17
| 17
| | 582.857
| 582.857
| | '''7/5'''
| '''7/5'''
| | '''24/17'''
| '''24/17'''
| | 17/12
| 17/12
| |  
|  
|-
|-
| | 18
| 18
| | 617.143
| 617.143
| | '''10/7'''
| '''10/7'''
| | '''17/12'''
| '''17/12'''
| | 24/17
| 24/17
| |  
|  
|-
|-
| | 19
| 19
| | 651.429
| 651.429
| | '''16/11'''
| '''16/11'''
| |  
|  
| |  
|  
| |  
|  
|-
|-
| | 20
| 20
| |685.714
|685.714
| |  
|  
| | '''3/2'''
| '''3/2'''
| |  
|  
| |  
|  
|-
|-
| | 21
| 21
| | 720
| 720
| |  
|  
| |  
|  
| | 3/2, '''32/21'''
| 3/2, '''32/21'''
| |  
|  
|-
|-
| | 22
| 22
| | 754.286
| 754.286
| | '''17/11''', 25/16
| '''17/11''', 25/16
| |  
|  
| |  
|  
| | '''14/9'''
| '''14/9'''
|-
|-
| | 23
| 23
| | 788.571
| 788.571
| | '''11/7'''
| '''11/7'''
| |  
|  
| |  
|  
| |  
|  
|-
|-
| | 24
| 24
| | 822.857
| 822.857
| | '''8/5'''
| '''8/5'''
| |  
|  
| |  
|  
| |  
|  
|-
|-
| | 25
| 25
| |857.143
|857.143
| | '''28/17'''
| '''28/17'''
| |  
|  
| | 5/3
| 5/3
| | '''18/11'''
| '''18/11'''
|-
|-
| | 26
| 26
| | 891.429
| 891.429
| |  
|  
| | '''5/3'''
| '''5/3'''
| |  
|  
| |  
|  
|-
|-
| | 27
| 27
| | 925.714
| 925.714
| | '''17/10'''
| '''17/10'''
| | '''12/7'''
| '''12/7'''
| |  
|  
| |  
|  
|-
|-
| | 28
| 28
| | 960
| 960
| | '''7/4'''
| '''7/4'''
| |  
|  
| |  
|  
| |  
|  
|-
|-
| | 29
| 29
| | 994.286
| 994.286
| |  
|  
| |  
|  
| |  
|  
| | '''16/9'''
| '''16/9'''
|-
|-
| | 30
| 30
| |1028.571
|1028.571
| | '''20/11'''
| '''20/11'''
| |  
|  
| |  
|  
| | '''9/5'''
| '''9/5'''
|-
|-
| | 31
| 31
| | 1062.857
| 1062.857
| |  
|  
| | '''11/6''', 15/8
| '''11/6''', 15/8
| |  
|  
| |  
|  
|-
|-
| | 32
| 32
| | 1097.143
| 1097.143
| | '''32/17'''
| '''32/17'''
| | '''28/15'''
| '''28/15'''
| | '''15/8'''
| '''15/8'''
| | '''17/9'''
| '''17/9'''
|-
|-
| | 33
| 33
| | 1131.429
| 1131.429
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|-
|-
| | 34
| 34
| | 1165.714
| 1165.714
| |  
|  
| |  
|  
| |  
|  
| |  
|  
|-
|-
|3
|3
Line 517: Line 588:
|}
|}


{| class="wikitable" style="text-align:center;"
{{15-odd-limit|35}}
|-
! Interval, complement
! Error (abs., in [[cent]]s)
|-
|[[7/5]] [[10/7]]
|0.3448
|-
|[[13/12]] [[24/13]]
|1.4296
|-
|[[9/8]] [[16/9]]
|1.8039
|-
|[[17/16]] [[32/17]]
|2.0984
|-
|[[11/8]] [[16/11]]
|2.7469
|-
|[[18/17]] [[17/9]]
|3.9024
|-
|[[11/9]] [[18/11]]
|4.5509
|-
|[[11/10]] [[20/11]]
|6.4247
|-
|[[14/11]] [[11/7]]
|6.0789
|-
|[[6/5]] [[5/3]]
|7.0703
|-
|[[7/6]] [[12/7]]
|7.4151
|-
|[[8/7]] [[7/4]]
|8.8259
|-
|[[14/13]] [[13/7]]
|8.8447
|-
|[[16/15]] [[15/8]]
|8.8742
|-
|[[5/4]] [[8/5]]
|9.1707
|-
|[[10/9]] [[9/5]]
|10.9747
|-
|[[12/11]] [11/6]]
|13.494
|-
|[[3/2]] [[4/3]]
|16.241
|-
|[[15/14]] [[28/15]]
|16.5858
|-
|
|
|}
 
 
=Rank two temperaments=


== Regular temperament properties ==
=== Rank-2 temperaments ===
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Periods
! Periods<br>per 8ve
 
! Generator
per octave
! Temperaments with<br>flat 3/2 (patent val)
! | Generator
! Temperaments with sharp 3/2 (35b val)
! | Temperaments with
! [[Mos scale]]s
 
flat 3/2 (patent val)
! | <span style="display: block; text-align: center;">Temperaments with sharp 3/2 (35b val)</span>
|-
|-
| | 1
| 1
| | 1\35
| 1\35
| |  
|  
| |  
|  
|  
|-
|-
| | 1
| 1
| | 2\35
| 2\35
| |  
|  
| |
|  
| [[1L 16s]], [[17L 1s]]
|-
|-
| | 1
| 1
| | 3\35
| 3\35
| |  
|  
| | [[Ripple|Ripple]]
| [[Ripple]]
| [[1L 10s]], [[11L 1s]], [[12L 11s]]
|-
|-
| | 1
| 1
| | 4\35
| 4\35
| | [[Greenwoodmic_temperaments#Secund|Secund]]
| [[Secund]]
| |  
|  
| [[1L 7s]], [[8L 1s]], [[9L 8s]], [[9L 17s]]
|-
|-
| | 1
| 1
| | 6\35
| 6\35
| colspan="2" | Messed-up [[Chromatic_pairs#Baldy|Baldy]]
| colspan="2" | [[Baldy]] (messed-up)
| [[1L 4s]], [[5L 1s]], [[6L 5s]], [[6L 11s]], [[6L 17s]], [[6L 23s]]
|-
|-
| | 1
| 1
| | 8\35
| 8\35
| |  
|  
| | Messed-up [[Orwell]]
| [[Orwell]] (messed-up)
| [[1L 3s]], [[4L 1s]], [[4L 5s]], [[9L 4s]], [[13L 9s]]
|-
|-
| | 1
| 1
| | 9\35
| 9\35
| | [[Myna|Myna]]
| [[Myna]]
| |  
|  
| [[1L 3s]], [[4L 3s]], [[4L 7s]], [[4L 11s]], [[4L 15s]], …, [[4L 27s]]
|-
|-
| | 1
| 1
| | 11\35
| 11\35
| | [[Muggles]]
| [[Muggles]]
| |  
|  
| [[3L 1s]], [[3L 4s]], [[3L 7s]] [[3L 10s]], [[3L 13s]], [[16L 3s]]
|-
|-
| | 1
| 1
| | 12\35
| 12\35
| |  
|  
| | [[Avicennmic_temperaments#Roman|Roman]]
| [[Roman]]
| [[2L 1s]], [[3L 2s]], [[3L 5s]], [[3L 8s]], [[3L 11s]], [[3L 14s]], [[3L 17s]], [[3L 20s]], …, [[3L 29s]]
|-
|-
| | 1
| 1
| | 13\35
| 13\35
| colspan="2" | Inconsistent 2.9'/7.5/3 [[Sensi]]
| colspan="2" | Inconsistent 2.9'/7.5/3 [[sensi]]
| [[2L 1s]], [[3L 2s]], [[3L 5s]], [[8L 3s]], [[8L 11s]], [[8L 19s]]
|-
|-
| | 1
| 1
| | 16\35
| 16\35
| |  
|  
| |
|  
| [[2L 1s]], [[2L 3s]], [[2L 5s]], [[2L 7s]], [[2L 9s]], [[11L 2s]], [[11L 13s]]
|-
|-
| | 1
| 1
| | 17\35
| 17\35
| |  
|  
| |
|  
| [[2L 1s]], [[2L 3s]], [[2L 5s]], [[2L 7s]], [[2L 9s]], [[2L 11s]], [[2L 13s]], [[2L 15s]], [[2L 17s]], [[2L 19s]], …, [[2L 31s]]
|-
|-
| | 5
| 5
| | 1\35
| 1\35
| |  
|  
| | [[Blackwood]] (favoring 7/6)
| [[Blackwood]] (favoring 7/6)
| [[5L 5s]], [[5L 10s]], [[5L 15s]], [[5L 20s]], [[5L 25s]]
|-
|-
| | 5
| 5
| | 2\35
| 2\35
| |  
|  
| | [[Blackwood]] (favoring 6/5 and 20/17)
| [[Blackwood]] (favoring 6/5 and 20/17)
| [[5L 5s]], [[5L 10s]], [[15L 5s]]
|-
|-
| | 5
| 5
| | 3\35
| 3\35
| |  
|  
| | [[Blackwood]] (favoring 5/4 and 17/14)
| [[Blackwood]] (favoring 5/4 and 17/14)
| [[5L 5s]], [[10L 5s]], [[10L 15s]]
|-
|-
| | 7
| 7
| | 1\35
| 1\35
| | [[Apotome_family|Whitewood]]/[[Apotome_family#Redwood|Redwood]]
| [[Whitewood]] / [[redwood]]
| |  
|  
| [[7L 7s]], [[7L 14s]], [[7L 21s]]
|-
|-
| | 7
| 7
| | 2\35
| 2\35
| | [[Greenwoodmic_temperaments#Greenwood|Greenwood]]
| [[Greenwood]]
| |  
|  
| [[7L 7s]], [[14L 7s]]
|}
|}


=Scales=
=== Commas ===
A good beginning for start to play 35-EDO is with the Sub-diatonic scale, that is a [[MOS]] of 3L2s: 9 4 9 9 4.
35et [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 35 55 81 98 121 130 }}.)
 
=Commas=
35 EDO [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 35 55 81 98 121 130 }}.)


{| class="commatable wikitable center-1 center-2 right-4 center-5"
{| class="commatable wikitable center-1 center-2 right-4 center-5"
|-
|-
! [[Harmonic limit|Prime <br> limit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Monzo]]
Line 698: Line 715:
| 3
| 3
| [[2187/2048]]
| [[2187/2048]]
| {{Monzo| -11 7 }}
| {{monzo| -11 7 }}
| 113.69
| 113.69
| Lawa
| Lawa
| Apotome, Whitewood comma
| Whitewood comma, apotome, Pythagorean chroma
|-
|-
| 5
| 5
| [[6561/6250]]
| [[6561/6250]]
| {{Monzo| -1 8 -5 }}
| {{monzo| -1 8 -5 }}
| 84.07
| 84.07
| Quingu
| Quingu
Line 712: Line 729:
| 5
| 5
| <abbr title="10077696/9765625">(15 digits)</abbr>
| <abbr title="10077696/9765625">(15 digits)</abbr>
| {{Monzo| 9 9 -10 }}
| {{monzo| 9 9 -10 }}
| 54.46
| 54.46
| Quinbigu
| Quinbigu
Line 719: Line 736:
| 5
| 5
| [[3125/3072]]
| [[3125/3072]]
| {{Monzo| -10 -1 5 }}
| {{monzo| -10 -1 5 }}
| 29.61
| 29.61
| Laquinyo
| Laquinyo
| Small diesis, Magic comma
| Magic comma, small diesis
|-
|-
| 7
| 7
| [[405/392]]
| [[405/392]]
| {{Monzo| -3 4 1 -2 }}
| {{monzo| -3 4 1 -2 }}
| 56.48
| 56.48
| Ruruyo
| Ruruyo
Line 733: Line 750:
| 7
| 7
| [[16807/16384]]
| [[16807/16384]]
| {{Monzo| -14 0 0 5 }}
| {{monzo| -14 0 0 5 }}
| 44.13
| 44.13
| Laquinzo
| Laquinzo
| Cloudy
| Cloudy comma
|-
|-
| 7
| 7
| [[525/512]]
| [[525/512]]
| {{Monzo| -9 1 2 1 }}
| {{monzo| -9 1 2 1 }}
| 43.41
| 43.41
| Zoyoyo
| Lazoyoyo
| Avicenna
| Avicennma
|-
|-
| 7
| 7
| [[126/125]]
| [[126/125]]
| {{Monzo| 1 2 -3 1 }}
| {{monzo| 1 2 -3 1 }}
| 13.79
| 13.79
| Zotrigu
| Zotrigu
| Starling comma, Septimal semicomma
| Septimal semicomma, starling comma
|-
|-
| 11
| 11
| [[99/98]]
| [[99/98]]
| {{Monzo| -1 2 0 -2 1 }}
| {{monzo| -1 2 0 -2 1 }}
| 17.58
| 17.58
| Loruru
| Loruru
Line 761: Line 778:
| 13
| 13
| [[66/65]]
| [[66/65]]
| {{Monzo| 1 1 -1 0 1 -1 }}
| {{monzo| 1 1 -1 0 1 -1 }}
| 26.43
| 26.43
| Thulogu
| Thulogu
Line 768: Line 785:
<references/>
<references/>


=Music=
== Scales ==
[http://soonlabel.com/xenharmonic/archives/2348 Little Prelude &amp; Fugue, "The Bijingle" by Claudi Meneghin]
* A good place to start using 35-EDO is with the sub-diatonic scale, that is a [[MOS]] of 3L2s: 9 4 9 9 4.
* Also available is the amulet scale{{idiosyncratic}}, approximated from [[magic]] in [[25edo]]: 3 1 3 3 1 3 4 3 3 1 3 4 3
* Approximations of [[gamelan]] scales:
** 5-tone pelog: 3 5 12 3 12
** 7-tone pelog: 3 5 7 5 3 8 4
** 5-tone slendro: 7 7 7 7 7
 
== Instruments ==
=== Lumatone ===
35edo can be played on the [[Lumatone]]. See [[Lumatone mapping for 35edo]]
 
=== Skip fretting ===
'''Skip fretting system 35 3 8''' is a [[skip fretting]] system for [[35edo]]. All examples on this page are for 7-string [[guitar]].
 
; Prime harmonics
1/1: string 2 open
 
2/1: string 3 fret 9 and string 6 fret 1
 
3/2: string 3 fret 4 and string 4 fret 13
 
5/4: string 3 fret 1, string 4 fret 10, and string 7 fret 2
 
7/4: string 4 fret 4
 
11/8: string 1 fret 8, string 4 open, and string 5 fret 9
 
13/8: string 1 fret 11, string 4 fret 3, and string 5 fret 12
 
17/16: string 2 fret 1 and string 3 fret 10
 
== Music ==
; [[dotuXil]]
* [https://www.youtube.com/watch?v=61ssLv9H6rk "Icebound Gallery of Refractions"] from [https://dotuxil.bandcamp.com/album/collected-refractions ''Collected Refractions''] (2024)
 
; [[E8 Heterotic]]
* [https://youtu.be/07-wj6BaTOw ''G2 Manifold''] (2020) – uses a combination of 5edo and 7edo, which can be classified as a 35edo subset.
 
; [[JUMBLE]]
* [https://www.youtube.com/watch?v=2qpsI26JfjY ''Penguins...?''] (2024)
 
; [[Chuckles McGee]]
* [https://www.archive.org/download/Transcendissonance/05Self-destructingMechanicalForest-CityOfTheAsleep.mp3 Self-Destructing Mechanical Forest] (in Secund[9])
 
; [[Claudi Meneghin]]
* [https://web.archive.org/web/20190412163316/http://soonlabel.com/xenharmonic/archives/2348'' Little Prelude &amp; Fugue, "The Bijingle"''] (2014)
* [https://www.youtube.com/watch?v=JPie2YDwA8I ''MicroFugue on Happy Birthday for Baroque Ensemble''] (2023)


[http://www.archive.org/download/Transcendissonance/05Self-destructingMechanicalForest-CityOfTheAsleep.mp3 Self-Destructing Mechanical Forest] by Chuckles McGee (in Secund[9])
; [[No Clue Music]]
* [https://www.youtube.com/watch?v=zMUQWdFRGao ''DarkSciFiThing''] (2024)


[[Category:35edo]]
[[Category:Listen]]
[[Category:Equal divisions of the octave]]
[[Category:listen]]
[[Category:theory]]
Retrieved from "https://en.xen.wiki/w/35edo"